klein ibhodlela

klein ibhodlela

Kwi-topology, igatsha lezibalo, klein ibhodlela iyisibonelo sendawo engafinyeleleki. Kuyi-multi-dimensional multi-dimensional lapho isistimu ingakwazi ukuchazwa ngokungaguquki ukuze kunqunywe ama-vector avamile. Ngokungakahleleki, indawo enohlangothi olulodwa, okuthi, uma idluliswa, ilandelwe ibuyele emsuka lapho umhambi ephenduka.

Kulesi sihloko sizokutshela konke odinga ukukwazi mayelana Klein ibhodlela, izici zayo kanye curiosities.

Izici eziyinhloko

ejabule klein

Ezinye izinto ezihlobene ezingafinyeleleki zifaka imichilo ye-Möbius kanye nezindiza zeqiniso zokuqagela. Imichilo ye-Mobius iyindawo elinganiselwe, kuyilapho amabhodlela e-Klein engenamingcele. Uma kuqhathaniswa, imbulunga iyindawo efinyeleleka ngokungenamkhawulo. Ibhodlela le-Klein lachazwa okokuqala ngo-1882 isazi sezibalo saseJalimane uFelix Klein.

Iqoqo lamabhodlela engilazi e-Klein aphephethwa ngesandla liboniswa e-Science Museum e-London, libonisa ukuhlukahluka okuningi kule timu ye-topological. Amabhodlela asuka ku-1995 futhi enziwa ngu-Alan Bennett ukuze enze imnyuziyamu.

Ibhodlela le-Klein ngokwalo aliwelani. Nokho, kukhona indlela yokubona ngeso lengqondo ibhodlela le-Klein eliqukethwe ngezilinganiso ezine. I-self-intersection ingasuswa ngokungeza ubukhulu besine endaweni enezinhlangothi ezintathu. Phusha kancane ingxenye yeshubhu equkethe impambanamgwaqo ephuma esikhaleni sangempela se-3D eduze nobukhulu besine. Isifaniso esiwusizo ukucabangela ijika elinqamula indiza. Ukuziphambana kwemigwaqo kungasuswa ngokuphakamisa imicu endizeni.

Ukucacisa, ake sithi sithatha isikhathi njengengxenye yesine. Cabangela indlela yokwakha igrafu esikhaleni se-xyzt. Isibalo esinamathiselwe (“Ukuziphendukela kwemvelo ngokuhamba kwesikhathi…”) sibonisa inguquko ewusizo yalo mfanekiso. Ku-t = 0, udonga lumila ndawana thize eduze "kwempambanomgwaqo." Ngemva kokuba isibalo sikhula, ingxenye yokuqala yodonga yaqala ukuhlehla, inyamalala njengekati laseCheshire, kodwa eshiya ukumamatheka kwakhe okubanzi. Lapho i-front front ifinyelela lapho ihlumela likhona, akukho lutho oluwela futhi ukukhula kuphelele ngaphandle kokubhoboza isakhiwo esikhona.

Izakhiwo zebhodlela le-Klein

klein izibalo ibhodlela

I-Klein flask iyindawo engafinyeleleki evame ukuvezwa njengeflask enentamo ende enentamo egobile edluliswa ukusuka ngaphakathi ukuze ivuleke njengesisekelo. Ukuma okuyingqayizivele kwebhodlela le-Klein kusho ukuthi inendawo eyodwa kuphela: ingaphakathi lilingana nengaphandle. Ibhodlela le-Klein alikwazi ukuba khona ngempela endaweni ye-Euclidean enezinhlangothi ezintathu, kodwa ukumelwa okufutha ingilazi kungasinika ukuqonda okuthakazelisayo. Akulona ibhodlela langempela leli, kodwa kuyasiza ukubona ngeso lengqondo lokho isazi sezibalo esingumJalimane uFelix Klein esasikucabanga lapho eqhamuka nombono webhodlela likaKlein.

Uma uphawu lunamathiselwe endaweni efinyeleleka kalula, njengengaphandle lendilinga, luzogcina umumo ofanayo kungakhathaliseki ukuthi uwuhambisa kanjani. Ukuma okukhethekile kwebhodlela le-Klein kukuvumela ukuthi ushelele uphawu ngezindlela ezihlukene: lungavela njengesithombe esibukweni saso endaweni efanayo. Le mpahla yebhodlela le-Klein yenza kube nzima ukuyiqondisa.

Ibhodlela le-Klein liqanjwe ngesazi sezibalo saseJalimane uFelix Klein. Umsebenzi kaFelix Klein wezibalo wamenza wajwayelana kakhulu namapheshana kaMöbius. Umdwebo we-Möbius uyiphepha elizuliswa uhhafu wokujika futhi lixhunywe ekugcineni ukuya ekugcineni. Lokhu kusonta kuguqula ishidi lephepha elijwayelekile libe indawo engafinyeleleki. U-Felix Klein wacabanga ukuthi uma ehlanganisa imicu ye-Möbius emibili emaphethelweni ayo, uzodala uhlobo olusha lwendawo enezici ezifanayo eziyinqaba: i-Klein surface noma ibhodlela le-Klein.

Ibhodlela le-Klein lichazwa njengendawo engafinyeleleki kalula ngenxa yokuthi uma uphawu lunamathiselwe phezulu, lingashelela ngendlela yokuthi likwazi ukubuyela endaweni efanayo nesithombe sesibuko.

Ingabe ibhodlela le-Klein lingenziwa empilweni yangempela?

ibhodlela elingapheli

Ngeshwa thina esifuna ukubona amabhodlela e-Klein angempela, awakwazi ukwakhiwa endaweni ye-Euclidean enezinhlangothi ezintathu esihlala kuyo. Xhuma imiphetho yemigqa emibili ye-Möbius ukuze wakhe i-Klein flask idala izimpambanomgwaqo ezingekho kumamodeli wetiyetha. Imodeli yangempela yebhodlela le-Klein bekufanele izidlulele yona ngesikhathi intamo isuka eceleni. Lokhu kusinika okuthile okungelona ngempela ibhodlela le-Klein elisebenzayo, kodwa kusemnandi ukulihlola.

Njengoba amaflaski e-Klein abelana ngezinto eziningi eziyinqaba nemicu ye-Möbius, labo bethu abangenakho ukuqonda okujulile kwezibalo ukuze baqonde ngempela ubunkimbinkimbi bamaflask e-Klein bangazama imicu ka-Felix Klein ethi Moebius Ukuthola okuthakazelisayo .

Izindawo zokuhlala e- Klein

UClifford Stoll uyindoda eyaklama leli bhodlela elikhulukazi i-Klein, elingama-106cm ubude, 62,2cm ububanzi kanye no-163,5cm ukuzungeza. Yakhiwe yi-Kildee Scientific Glass phakathi kuka-2001 no-2003.

Igama langempela lale nto kwakungeyona i-Klein Flask (i-Kleinsche Flasche yesiJalimane), kodwa i-Klein Surface (i-Kleinsche Fläche yesiJalimane). Ukuhunyushwa kwento yokuqala okubhekiselwa kuyo kusuka eJalimane kuya esiNgisini amagama adidekile. Ngenxa yokubukeka kwe-3D enikeza isikhumbuzo sebhodlela, akekho owabona iphutha.

Uma sihlukanisa ibhodlela le-Klein kabili ngendiza yalo yokulinganisa, sakha imichilo emibili ye-Möbius, ngayinye eyisithombe sesibuko somunye (njengokungathi omunye uzibuka esibukweni). Bese, ibhodlela le-Klein liyisibonelo sendawo engafinyeleleki, njengomdwebo we-Möbius. Awunawo omunye umsebenzi ngaphandle kokuwumela. Izindawo ezisempumalanga noma ezingafinyeleleki ziyimiqondo ye-topological. Zombili ziyizibonelo zezindawo ezinohlangothi olulodwa, ngoba azikwazi ukuhamba. Umlingo wayo usekukwazini ukuwumboza ngokuphelele ngendlela eqhubekayo, ehlanganisa wonke amaphuzu awubumbayo.

Ngithemba ukuthi ngalolu lwazi ungafunda kabanzi mayelana nebhodlela le-Klein nezici zalo.


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  1. Ubhekele imininingwane: Miguel Ángel Gatón
  2. Inhloso yedatha: Lawula Ugaxekile, ukuphathwa kwamazwana.
  3. Ukusemthethweni: Imvume yakho
  4. Ukuxhumana kwemininingwane: Imininingwane ngeke idluliselwe kubantu besithathu ngaphandle kwesibopho esisemthethweni.
  5. Isitoreji sedatha: Idatabase ebanjwe yi-Occentus Networks (EU)
  6. Amalungelo: Nganoma yisiphi isikhathi ungakhawulela, uthole futhi ususe imininingwane yakho.